Question

A cart of mass $M$ is at rest on a frictionless horizontal surface and a pendulum bob of mass $m$ hangs from the roof of the cart. The string breaks, the bob falls on the floor, makes several collisions on the floor and finally lands up in a small slot made in the floor. The horizontal distance between the string and the slot is $L$. Find the displacement of the cart during this process.

Answer 1

Initial com at $x$

$x=\frac{ML}{m+M}$

Finally

$x=\frac{(M+m)(L-x)}{(M+m)}\frac{ML}{m+M}=\frac{(M+m)(L-x)}{M+m)}ML=ML+mL-(M+m)xx=\frac{mL}{(M+m)}$

cart move distance $x$ left.